An article in the newspaper about Henry's daughter Mary Ann mentioned in his Will - talks about his arrival in Australia being in SA and then going to Victoria. From this article I have also provided a possible link to the date and ship he arrived on.
The Advertiser (Adelaide, SA : 1931 - 1954) Previous issue Wednesday 27 January 1937
Descended From Captain Cook
Mrs. M. A. Trewren, of First avenue, Royston Park, claims to be a collateral descendant of Captain Cook, the dis- coverer of Australia. Her great grand-
mother was a niece of the navigator. Mrs. Trewren's father, through whom she claims descent, came to South Aus tralia in 1839, but stayed for only four years. He settled in Victoria, and Mrs. Trewren was born there. She married 47 years ago, and has since lived in Adelaide. At her home Mrs. Trewren has a number of historical relics, including etchings of Captain Cook and Admiral Sir Charles Saunders, a direct ancestor. She also has a remarkable parchment map in the form of a sphere, which can be inflated. The map was drawn by her father, Mr. H. Saunders at a Bristol Academy at the age of 14. The cartography is excellent, and the colors look as if they had been used only a year or so ago.
This might be his arrival.
South Australian Passenger Lists
Shipping arrivals and immigration 1803 to 1854+
SAUNDERS Henry arrived in SA 1839-07-24 aboard William (2) from Launceston [Source:23(1/2),38]